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#1 2013-03-25 05:38:39

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

One biased coin

Infront of you lie 10 coins one of which is biased
You take a random coin and toss it 5 times.
It results H for all 5 times
Now, what is the probability that this coin is biased?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2013-03-25 08:06:36

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi Agnishom;

Was the probability of head using the biased coin provided?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-03-25 14:28:28

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

The biased coin always results in a head


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2013-03-25 20:08:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi;


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-03-25 21:01:13

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Logic?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#6 2013-03-25 21:16:05

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

It seems that this is not correct. Do you want the exact wording of the problem?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#7 2013-03-25 21:23:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

I just had a small conversation about this with anonimnystefy. I thought I was a frequentist but no, I am a Bayesian!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#8 2013-03-25 21:30:33

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

I can't understand sad


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#9 2013-03-25 21:32:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

It is Bayesian analysis. It is on the difficult side if you are seeing it for the first time.

I will attempt to explain it but first, did I get the right answer?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#10 2013-03-25 21:33:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,836

Re: One biased coin

If it is correct, it is a simple application of Bayes' theorem.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#11 2013-03-25 21:34:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Yes, that is what I used.

Agnishom wrote:

It seems that this is not correct. Do you want the exact wording of the problem?

Yes!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#12 2013-03-25 21:38:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,836

Re: One biased coin

It seems you posted while I was posting.

It is interesting how weird a result it can produce!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#13 2013-03-25 21:42:47

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Okay I attach it.

View Image: image.jpg

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#14 2013-03-25 21:43:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi;
Wait a minute! This question say fair coin. Your original question asked for biased coin.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#15 2013-03-25 21:46:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,836

Re: One biased coin

Everything is good except the fact that you got the guy the probability of the coin being biased!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#16 2013-03-25 21:49:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Agnishom wrote:

Now, what is the probability that this coin is biased?

That is what his original question asked for in post #1.

Just take the complement. 9 / 41 and add that. You get 50.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#17 2013-03-25 21:58:09

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Okay 50 thanks smile

Anyway, what I actually need to know is how to do the problem...
Which I can't make any idea of


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#18 2013-03-25 21:59:39

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi Agnishom;

There is a formula to do these. You just plug in. This makes it very simple.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#19 2013-03-25 22:00:55

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Please teach me the formula


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#20 2013-03-25 22:08:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi;

X = hhhhh



In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#21 2013-03-25 22:12:51

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

X occur?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#22 2013-03-25 22:15:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi;

Please look at post #20.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#23 2013-03-25 22:31:32

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Thanks its womderful


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#24 2013-03-25 22:34:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,622

Re: One biased coin

Hi;

Do you see how each value for the formula is computed?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#25 2013-03-25 22:59:59

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,319
Website

Re: One biased coin

Yes


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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